--- a/progs/while.scala	Mon Nov 14 15:50:42 2016 +0000
+++ b/progs/while.scala	Fri Dec 16 11:13:41 2016 +0000
@@ -87,6 +87,19 @@
   }
 }
 
+def len(xs: List[(Int, Int)]): Int = xs match {
+  case Nil => 0
+  case (1, x)::xs => len(xs) + 1
+  case (_, x)::xs => len(xs) 
+}
+
+def fst(p: (Int, Int)): Int = p match {
+  case Nil => 0
+  case (1, x)::xs => len(xs) + 1
+  case (_, x)::xs => len(xs) 
+}
+
+
 
 // arithmetic expressions
 lazy val AExp: Parser[List[Token], AExp] =